Cryptology ePrint Archive: Report 2020/720

Fast algebraic immunity of Boolean functions and LCD codes

Sihem Mesnager and Chunming Tang

Abstract: Nowadays, the resistance against algebraic attacks and fast algebraic attacks are considered as an important cryptographic property for Boolean functions used in stream ciphers. Both attacks are very powerful analysis concepts and can be applied to symmetric cryptographic algorithms used in stream ciphers. The notion of algebraic immunity has received wide attention since it is a powerful tool to measure the resistance of a Boolean function to standard algebraic attacks. Nevertheless, an algebraic tool to handle the resistance to fast algebraic attacks is not clearly identified in the literature. In the current paper, we propose a new parameter to measure the resistance of a Boolean function to fast algebraic attack. We also introduce the notion of fast immunity profile and show that it informs both on the resistance to standard and fast algebraic attacks. Further, we evaluate our parameter for two secondary constructions of Boolean functions. Moreover, A coding-theory approach to the characterization of perfect algebraic immune functions is presented. Via this characterization, infinite families of binary linear complementary dual codes (or LCD codes for short) are obtained from perfect algebraic immune functions. The binary LCD codes presented in this paper have applications in armoring implementations against so-called side-channel attacks (SCA) and fault non-invasive attacks, in addition to their applications in communication and data storage systems.

Category / Keywords: secret-key cryptography / Boolean function, (Fast) Algebraic immunity, Algebraic attack, Fast algebraic attack, Fault injection attack Side-channel attack, LCD code, Reed-Muller code,

Date: received 15 Jun 2020

Contact author: tangchunmingmath at 163 com

Available format(s): PDF | BibTeX Citation

Version: 20200616:065832 (All versions of this report)

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